Transforms - Convolution

 
   
     
       

Laplace Transform

       

Laplace Convolution Theorem

       

          The convolution theorem under Laplace Transform provides a way to compute the Laplace Transform of the convolution of two functions, turning it into multiplication.        

        Laplace Convolution Formula.      
     
       
         

Formula:

         
           

\[ \mathcal{L}\{f * g\}(s) = F(s) \cdot G(s) \]

           

\[ f * g = \int_0^{t} f(t - z) g(z) dz \]

         
         

Applications:

         
               
  • Solving linear time-invariant systems.
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  • Modeling systems with memory or delay.
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  • Control theory and differential equation modeling.
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